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Biodiversity, Shapely Value and Phylogenetic Trees: Some Remarks

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  • Hubert Stahn

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper explores the main differences between the Shapley Values of a set of taxa introduced by Haake et al. [4] and Fuchs and Jin [3], the latter having been found identical to the Fair Proportion Index (Redding and Mooers [10]). In line with Shapley [13], we identify the cooperative game basis for each of these two classes of phylogenetic games and use them (i) to construct simple formulas for these two Shapley values and (ii) to compare these different approaches. Using the set of weights of a phylogenetic tree as a parameter space, we then discuss the conditions under which these two values coincide and, if they are not the same, revisit Hartman's [5] convergence result. Finally, we compare the species ranking induced by these two values. Considering the Kendal and the Spearman rank correlation coefficient, simulations show that these rankings are strongly correlated.

Suggested Citation

  • Hubert Stahn, 2017. "Biodiversity, Shapely Value and Phylogenetic Trees: Some Remarks," Working Papers halshs-01630069, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01630069
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01630069
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    References listed on IDEAS

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    1. Kleinberg, Norman L. & Weiss, Jeffrey H., 1985. "A new formula for the Shapley value," Economics Letters, Elsevier, vol. 17(4), pages 311-315.
    2. Haake, Claus-Jochen & Kashiwada, Akemi & Su, Francis Edward, 2016. "The Shapley Value of Phylogenetic Trees," Center for Mathematical Economics Working Papers 363, Center for Mathematical Economics, Bielefeld University.
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    Cited by:

    1. Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "Mathematical indices for the influence of risk factors on the lethality of a disease," ThE Papers 21/02, Department of Economic Theory and Economic History of the University of Granada..

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    More about this item

    Keywords

    biodiversity; phylogenetic trees; Shapley value; Fair Proportion index;
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